$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 3x + 4$ and $ JT = 5x + 2$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {3x + 4} = {5x + 2}$ Solve for $x$ $ -2x = -2$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 3({1}) + 4$ $ JT = 5({1}) + 2$ $ CJ = 3 + 4$ $ JT = 5 + 2$ $ CJ = 7$ $ JT = 7$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {7} + {7}$ $ CT = 14$